List of top Questions asked in KEAM

A horizontal force is exerted on a 20 kg box to slide it up on an inclined plane with an angle of 30°. The frictional force retarding the motion is 80 N. If the box moves with a constant speed, then the magnitude of the force is:(Take g=10 ms-2)

If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\)  in the ratio \(α:1\),then the value of \(α\) is ? 
For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an
Consider the Linear Programming Problem:
Minimize 3x1+4x2 +2x3
subject to
x1+x2+x3≤6
x1+2x2+x3≤10
x1,x2,x3≥0.
Then, the number of basic solutions are
A wheel is rolling on a plane surface. A point on the rim of the wheel at the same level as the Centre has a speed of 4m/s. The speed of the Centre of the wheel is:
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is
If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

A projectile is thrown at a speed V and at an angle with the horizontal. If the speed at its maximum height is \(\frac{V}{3}\),then the value of tan θ is: 

\(\text{The value of    } cosec20°tan60°-sec20° \text{is }\)
Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) is 
The number of electrons in one mole of methane:
The mean deviation about the median for the data \(3,5,9,3,8,10,7\) is ?
If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is 
The number of S-S bonds and the number of lone pairs in S8 molecule,respectively,are:
In an oil drop experiment, 'n' numbers of electrons are stripped from an oil drop to make it positively charged. A vertical electric field of magnitude 4.9x1014 N/C is applied to balance the force due to gravity on the oil drop. If the mass of oil drop is 80 μg,the value of 'n' will be:(Take g =9.8 m/s2 and charge of an electron = 1.6 x 10-19 C)
A planet has an escape speed of 10km/s,The radius of the planet is 10,000km. The acceleration due to gravity of the planet at its surface is:
The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is 
A system of ideal gas undergoes a thermodynamic process in which the initial pressure and volume are equal to the final pressure and volume. Let △Q is the heat supplied to the system,△W is the work done by the system and △U is the change in internal energy. The correct option is: 

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is 

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?
Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is 
An ideal gas is kept in a closed container. If the temperature is doubled and the volume of the container is reduced to half, the gas pressure is:
A series LCR circuit consists of a variable capacitor connected to an inductor of inductance 50 mH,resistor of resistance 100 Ω and an AC source of angular frequency 500 rad/s. The value of capacitance so that maximum current may be drawn into the circuit is:
Find the effective resistance between points A and B. Each resistance is equal to R.